Pfaffian Hybrid Systems

  • Margarita Korovina
  • Nicolai Vorobjov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3210)


It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o-minimal systems defined by Pfaffian functions, either implicitly (via triangular systems of ordinary differential equations) or explicitly (by means of semi-Pfaffian maps). We give explicit upper bounds on the sizes of bisimulations as functions of formats of initial dynamical systems. We also suggest an algorithm with an elementary (doubly-exponential) upper complexity bound for computing finite bisimulations of these systems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Margarita Korovina
    • 1
  • Nicolai Vorobjov
    • 2
  1. 1.A.P.Ershov Institute of Informatics Systems, Russian Academy of Sciences 
  2. 2.Department of Computer ScienceUniversity of BathBathEngland

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